function maxangle = nonlinair1 
%NONLINAIR1: MATLAB function M-file that computes the angle 
%of maximum distance in the case of nonlinear air resistance.
%
%Author: Peter Howard
maxangle = fminsearch(@negdist, 45.); % 40.685);
%Use the angle of maximum distance for the case of linear 
%air resistance as initial guess. 
%I.e., minimize the negative of the distance
%
function d = negdist(theta)
%DIST: MATLAB function M-file that takes an angle theta as input
%and returns the horizontal distance a dart with initial speed
%v0 and air resistance coefficient b
v0 = 12.2540; b=.0645; g = 9.81;
rhs = @(t,y) [y(2);-b*sqrt(y(2)^2+y(4)^2)*y(2);y(4);-g-b*sqrt(y(2)^2+y(4)^2)*y(4)];
options=odeset('Events',@subevents);
[t,y,te,ye,ie]=ode45(rhs,[0 20],[0;v0*cosd(theta);.18;v0*sind(theta)],options);
d = - ye(end,1);
%
function [lookfor stop direction]=subevents(t,y)
lookfor = y(3);
stop = 1;
direction = -1;